Cam design per VDI 2143
Design motion laws for cam mechanisms per VDI 2143 and check pressure angle, curvature, lift-off and manufacturability right in your browser. The motion law is the 4-5-6-7 polynomial: velocity, acceleration and jerk are zero at the segment boundaries, so the transitions into the dwells are free of jerk peaks and avoid unnecessary vibration excitation. How to use it: set up the motion plan (rise, dwell and return segments with angle range and stroke), enter base circle, roller, mass, spring and speed, review the assessment criteria and export the finished contour to your CAD system: as a SolidWorks curve (renamed to .dat also for Siemens NX), as Excel points for the Inventor point import or as a universal XYZ CSV for CAD systems such as FreeCAD, CATIA and Fusion 360. The calculator provides motion diagrams and the cam contour, live with every input.
Calculation
Results
Calculating …
CAD import of the cam contour
The origin of all export files is the cam rotation axis: the contour is a closed point loop around (0,0), so coordinates run from −(base circle + lift) to +(base circle + lift). The rotation axis then sits directly on the sketch origin in CAD.
- SolidWorks: Insert > Curve > Curve Through XYZ Points, then select the file (values are interpreted in the document units, set the template to millimetres).
- Inventor: use the Excel file, 3D sketch > Insert points; sheet 1 follows the Inventor convention (unit mm in cell A1, XYZ without header).
- Siemens NX: rename the SolidWorks file to .dat, then Spline through points > points from file.
- Fusion 360: import the CSV with the ImportSplineCSV sample script. Note that the script interprets values as centimetres; scale by 0.1 afterwards or adapt the script to millimetres.
- FreeCAD (Curves workbench/macro) and CATIA (GSD point-import macro): use the universal XYZ CSV with decimal points.
Calculation in your browser, inputs go to our server only when you export or save.
Formulas and fundamentals
Motion law per VDI 2143
The guideline VDI 2143 describes motion laws for cam mechanisms. The calculator uses the polynomial 4-5-6-7 with the normalized profile:
At the segment boundaries (u = 0 and u = 1) velocity, acceleration and jerk are zero, so the transitions are C3-continuous and jerk-free.
Pressure angle
The pressure angle α describes the force direction between cam and roller. It is evaluated over the full revolution and checked against the configured limit; 30 degrees is a common maximum. In addition the calculator reports the base circle radius required to satisfy the limit.
Curvature, undercut and contact force
The radius of curvature of the pitch curve follows from the polar form with r = r_base + s. If its minimum falls below the roller radius, undercut occurs. The calculator also checks the curvature of the machined contour against cutter radius and safety factor, and the contact force from inertia, spring and preload against lift-off.
Worked example
The default project lifts the follower by 40 mm within 60 degrees, dwells, returns in two segments of 10 mm and 30 mm and dwells until 360 degrees. Base circle radius 130 mm, roller radius 10 mm, speed 60 rpm, mass 2 kg, spring rate 30 N/mm, preload 150 N.
The calculator returns a maximum pressure angle of 29.29 degrees (limit 30 degrees), a minimum pitch curve radius of curvature of 37.70 mm and a resulting safety factor of 3.77 with respect to the roller radius. All six criteria pass; the cam is free of undercut and manufacturable.
Frequently asked questions
What is VDI 2143?
VDI 2143 is a guideline for motion laws in cam mechanisms. It defines normalized transfer functions and their characteristic values for cam design, including polynomial, sinusoidal and trapezoidal laws.
Why is the polynomial 4-5-6-7 jerk-free?
With the polynomial 4-5-6-7 not only velocity and acceleration but also jerk (the third derivative) are zero at both segment boundaries. The motion is C3-continuous, so transitions to dwells produce no jerk peaks and no unnecessary vibration excitation.
Which pressure angle limit should I use?
For translating roller followers a maximum of 30 degrees is common; oscillating levers allow up to about 45 degrees. Larger pressure angles create high lateral forces in the follower guide and can lead to jamming. The calculator checks the maximum over the full revolution against the configured limit.
What is undercut and how do I avoid it?
Undercut occurs when the minimum radius of curvature of the pitch curve is smaller than or equal to the roller radius. The roller can no longer follow the intended path and the contour is distorted. Remedies are a larger base circle, a smaller roller or a gentler motion law with a larger drive angle.
How large does the base circle need to be?
The base circle must be large enough to satisfy the pressure angle limit and the curvature criteria. The calculator reports the required base circle radius for the pressure angle limit: r_base ≥ max(|s′| / tan α_allow − s) over the revolution. In addition the safety factor from radius of curvature and roller radius is checked.
Which export formats are available?
Each format targets a specific CAD import path. SolidWorks: load the SolidWorks curve directly via Insert, Curve, Curve Through XYZ Points; the same file works in Siemens NX (spline through points, points from file) after renaming the extension to .dat. Autodesk Inventor: load the Excel points in a 3D sketch via Insert Points; sheet 1 follows the Inventor requirements (unit mm in A1, X/Y/Z points from row 2, no header row) and sheet 2 additionally holds the angle/X/Y table for verification. FreeCAD, CATIA and Fusion 360: read the XYZ CSV (x,y,z with point decimals, no header) via point import macros or add-ins. All point files contain the curvature-optimised, closed contour (first point = last point, dense points in tight radii). A verification PDF with inputs, characteristic values and criteria completes the set.
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